The tree Constraint

  • Nicolas Beldiceanu
  • Pierre Flener
  • Xavier Lorca
Conference paper

DOI: 10.1007/11493853_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3524)
Cite this paper as:
Beldiceanu N., Flener P., Lorca X. (2005) The tree Constraint. In: Barták R., Milano M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2005. Lecture Notes in Computer Science, vol 3524. Springer, Berlin, Heidelberg

Abstract

This article presents an arc-consistency algorithm for the tree constraint, which enforces the partitioning of a digraph \(\mathcal{G}\) = (\(\mathcal{V},\mathcal{E}\)) into a set of vertex-disjoint anti-arborescences. It provides a necessary and sufficient condition for checking the tree constraint in \(\mathcal{O}(|\mathcal{V}| + |\mathcal{E}|)\) time, as well as a complete filtering algorithm taking \(\mathcal{O}(|\mathcal{V}| \cdot |\mathcal{E}|)\) time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Nicolas Beldiceanu
    • 1
  • Pierre Flener
    • 2
    • 3
  • Xavier Lorca
    • 1
  1. 1.École des Mines de NantesLINA FREE CNRS 2729Nantes Cedex 3France
  2. 2.Department of Information TechnologyUppsala UniversityUppsalaSweden
  3. 3.The Linnaeus Centre for BioinformaticsUppsala UniversityUppsalaSweden

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